From the theoretical point of view, spectral embeddings are supported by a classical linear algebra result, the Eckart-Young
theorem [1]}. It establishes that the best rank \(k\)  approximation in the Frobenius norm of a real, symmetric and
positive semi-definite matrix \(W\)  of dimension \(n\)  is the matrix
\(E^k=\widetilde{U}^k(\widetilde{U}^k)^t\) 
